North Korea marked the anniversary of the birthday of its founding father and Kim's grandfather, Kim Il Sung, as a national holiday on April 15, but Kim was not seen in attendance.
Daily NK, a speciality website run mostly by North Korean defectors, cited unidentified sources inside the isolated state saying Kim is recovering at a villa in the Mount Kumgang resort county of Hyangsan on the east coast after getting the procedure on April 12 at a hospital there.
Reporting from inside North Korea is notoriously difficult, especially on matters concerning the country's leadership, given tight controls on information.
South Korea's Unification Ministry, which handles inter-Korean affairs, declined to comment on the report.
Kim's health has deteriorated in recent months due to heavy smoking, obesity and overwork, the Daily NK report said.
"My understanding is that he had been struggling (with cardiovascular problems) since last August but it worsened after repeated visits to Mount Paektu," a source was quoted as saying, referring to the country's sacred mountain.
But Kim presided over a meeting on April 11, discussing coronavirus prevention and electing his sister as an alternate member of the political bureau of the ruling Workers' Party, according to the North's official Korean Central News Agency. And state media have since reported he sent greetings to Syrian President Bashar Assad and Cuban President Miguel Diaz-Canel as well as "birthday spreads" to two North Korean officials and a new centenarian.
The rumour suggests Kim left for the hospital after presiding over the meeting of the ruling Workers' Party's politburo on April 11, where Kim was publicly last seen, the report said.
It's unclear what would happen if Kim is sidelined by health problems or dies. Cheong Seong-Chang, an analyst at the private Sejong Institute in South Korea, said political upheaval would be unlikely as Kim's sister, Kim Yo Jong, is already exercising significant influence within the government, and most members of North Korea's leadership share an interest with the Kim family in maintaining the North's system.
Pyongyang fired multiple short-range missiles last week which Seoul officials said were also part of the Kim Il Sung birthday celebration. Such military events would usually be observed by Kim, but there was no KCNA report on the test at all.
"We have no information to confirm regarding rumors about Chairman Kim Jong Un's health issue that have been reported by some media outlets," South Korean presidential spokesman Kang Min-seok said.
"Also, no unusual developments have been detected inside North Korea."
A US official said the White House was aware before the reports appeared that Kim's health might be precarious. The official said the US had information that Kim may have undergone surgery and that complications may have rendered him "incapacitated or worse." But, the official stressed that the US had nothing to confirm the surgery had taken place or that any complications had occurred.
The US official, who was not authorized to discuss the matter publicly and spoke on condition of anonymity, would not elaborate on where the information came from or when it had been received.
The White House and State Department had no comment.
This is not the first time the North Korean's leader's absence has sparked talks of poor health.
There was a time in 2014 where Kim was not seen in public for more than a month and when he finally returned he was using a cane to walk.
It was later reported that he had a cyst removed from his ankle.
